Nonlinear analysis of structures

To understand fundamental mathematical and mechanical formulations of the nonlinear structural analysis.

Student is able to independently create and analyze geometrically and materially nonlinear models of continua and structures.

Introduction to the nonlinear analysis. Sources of nonlinear behavior of structures. Lagrange and Euler description of displacement. Lagrangian finite one-dimensional elements - description of deformation and stress fields. Geometric nonlinearity of structures - Total Langrangian and Updated Langrangian. Formulation of geometrically nonlinear problems - nonlinear analysis of beams and shells. Bifurcation stability of beams and shells. Procedures for solving nonlinear equations (Newton-Rapson, modified Newton-Rapson, Arc length method). Review of models for the analysis of material nonlinearity (nonlinear elasticity, one - dimensional plasticity, multiaxial plasticity, viscoelasticity ...). Solution procedures and stability of a solution.

1. K.J. Bathe, „Finite Element Procedures”, Prentice-Hall, 1996

   (Original)

2. T. Belytschko,W.K. Liu, B. Moran, „Nonlinear Finite Elements for Continua and Structures”,Wiley, 2000

   (Original)

3. M.A. Crisfield, „Non-Linear Finite Element Analysis of solids and Structires”,Wiley, 1991

   (Original)

4. J. Jarić, „Mehanika kontinuuma”, Građevinska knjiga, 1988

   (Original)

5. G. Radenković, „Konačne rotacije i deformacije u izogeometrijskoj teoriji nosača”, Univerzitet u Beogradu-Arhitektonski fakultet, 2017

   (Original)

Calculation and defence of the semestral assignment (50%)
Oral exam (50%)

Auditory lectures and individual work with students